Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-5x+3y &= 7 \\ 8x-2y &= -4\end{align*}$
Solution: Begin by moving the $y$ -term in the second equation to the right side of the equation. $8x = 2y-4$ Divide both sides by $8$ to isolate $x$ $x = {\dfrac{1}{4}y - \dfrac{1}{2}}$ Substitute this expression for $x$ in the first equation. $-5({\dfrac{1}{4}y - \dfrac{1}{2}}) + 3y = 7$ $-\dfrac{5}{4}y + \dfrac{5}{2} + 3y = 7$ Simplify by combining terms, then solve for $y$ $\dfrac{7}{4}y + \dfrac{5}{2} = 7$ $\dfrac{7}{4}y = \dfrac{9}{2}$ $y = \dfrac{18}{7}$ Substitute $\dfrac{18}{7}$ for $y$ in the top equation. $-5x+3( \dfrac{18}{7}) = 7$ $-5x+\dfrac{54}{7} = 7$ $-5x = -\dfrac{5}{7}$ $x = \dfrac{1}{7}$ The solution is $\enspace x = \dfrac{1}{7}, \enspace y = \dfrac{18}{7}$.